Mann-Whitney U test in SciPy - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the Mann-Whitney U test used for?

It is a test to compare two groups to see if one tends to have larger values than the other, without assuming the data follows a normal distribution.

beginner

What kind of data does the Mann-Whitney U test work with?

It works with two independent samples of ordinal or continuous data that do not need to be normally distributed.

beginner

In Python's scipy library, which function performs the Mann-Whitney U test?

The function is scipy.stats.mannwhitneyu.

beginner

What does the p-value from the Mann-Whitney U test tell us?

It tells us how likely it is to see the observed difference between groups if there was actually no difference.

beginner

What is the null hypothesis in the Mann-Whitney U test?

The null hypothesis is that the two groups come from the same distribution, meaning no difference in their values.

What does the Mann-Whitney U test compare?

A Two independent groups without assuming normal distribution

B Two paired groups assuming normal distribution

C More than two groups with normal distribution

D Correlation between two variables

The Mann-Whitney U test compares two independent groups without assuming the data is normally distributed.

Which scipy function runs the Mann-Whitney U test?

A scipy.stats.ttest_ind

B scipy.stats.mannwhitneyu

C scipy.stats.chi2_contingency

D scipy.stats.pearsonr

scipy.stats.mannwhitneyu is the function for the Mann-Whitney U test.

What does a small p-value from the Mann-Whitney U test indicate?

A Strong evidence that the two groups differ

B No difference between groups

C Data is normally distributed

D Test was not performed correctly

A small p-value means strong evidence against the null hypothesis, suggesting the groups differ.

Which assumption is NOT required for the Mann-Whitney U test?

A Samples are independent

B Groups have similar shapes

C Data is ordinal or continuous

D Data is normally distributed

The Mann-Whitney U test does NOT require data to be normally distributed.

If the Mann-Whitney U test returns U=0, what does it mean?

A Test failed to run

B Both groups have identical values

C One group has all smaller values than the other

D Groups are perfectly correlated

U=0 means all values in one group are smaller than all values in the other group.

Explain in your own words what the Mann-Whitney U test does and when you would use it.

Think about comparing two groups when you can't assume normal data.

Describe how to perform the Mann-Whitney U test using scipy and interpret the results.

Focus on the function call and what the output numbers mean.

Practice

1. What is the main purpose of the Mann-Whitney U test in data analysis?

easy

A. To test if a single sample mean equals a known value

B. To compare two independent groups without assuming normal distribution

C. To measure the correlation between two variables

D. To analyze the variance among multiple groups

Solution

1. Step 1: Understand the test purpose

   The Mann-Whitney U test is a non-parametric test used to compare two independent groups.

2. Step 2: Identify the key feature

   It does not assume the data follows a normal distribution, unlike t-tests.

3. Final Answer:

   To compare two independent groups without assuming normal distribution -> Option B

4. Quick Check:

   Non-parametric comparison = C [OK]

Hint: Remember: Mann-Whitney compares two groups without normality [OK]

Common Mistakes:

• Confusing it with correlation tests
• Assuming it compares means only
• Using it for more than two groups

2. Which of the following is the correct way to import the Mann-Whitney U test function from scipy?

easy

A. import scipy.mannwhitneyu as mw

B. import mannwhitneyu from scipy.stats

C. from scipy import mann_whitney_u_test

D. from scipy.stats import mannwhitneyu

Solution

1. Step 1: Recall scipy.stats module functions

   The Mann-Whitney U test function is named mannwhitneyu and is inside scipy.stats.

2. Step 2: Check correct import syntax

   The correct Python import syntax is from scipy.stats import mannwhitneyu.

3. Final Answer:

   from scipy.stats import mannwhitneyu -> Option D

4. Quick Check:

   Correct import syntax = B [OK]

Hint: Use 'from scipy.stats import mannwhitneyu' to import [OK]

Common Mistakes:

• Using wrong module or function name
• Incorrect import syntax
• Trying to import with 'import ... as' incorrectly

3. What will be the output of the following code snippet?

from scipy.stats import mannwhitneyu
x = [1, 3, 5]
y = [2, 4, 6]
stat, p = mannwhitneyu(x, y)
print(round(stat, 2), round(p, 3))

medium

A. 3.0 0.5

B. 4.5 0.25

C. 6.0 0.05

D. 0.0 1.0

Solution

1. Step 1: Understand the data and test

   Lists x and y have values [1,3,5] and [2,4,6]. Mann-Whitney U test compares ranks between these two groups.

2. Step 2: Calculate Mann-Whitney U statistic and p-value

   Using scipy, the U statistic is 3.0 and p-value is 0.5 (two-sided test by default).

3. Final Answer:

   3.0 0.5 -> Option A

4. Quick Check:

   U=3.0, p=0.5 from scipy output [OK]

Hint: Run code to get exact U and p values quickly [OK]

Common Mistakes:

• Mixing up U statistic with p-value
• Rounding incorrectly
• Assuming p-value is always small

4. Identify the error in this Mann-Whitney U test code and select the fix:

from scipy.stats import mannwhitneyu
x = [1, 2, 3]
y = [4, 5, 6]
stat, p = mannwhitneyu(x, y, alternative='greater')
print(stat, p)

medium

A. Replace mannwhitneyu with mann_whitney_u

B. Change 'alternative' to 'two-sided'

C. No error; code runs correctly

D. Use 'alternative="greater"' with capital G

Solution

1. Step 1: Check function parameters

   The mannwhitneyu function accepts an alternative parameter with values 'two-sided', 'less', or 'greater'.

2. Step 2: Verify code correctness

   Using alternative='greater' is valid and the function call is correct.

3. Final Answer:

   No error; code runs correctly -> Option C

4. Quick Check:

   Correct parameter usage = D [OK]

Hint: Check scipy docs for valid 'alternative' values [OK]

Common Mistakes:

• Using wrong alternative string case
• Trying to use non-existent function names
• Assuming default alternative is 'greater'

5. You have two small samples with skewed data: a = [2, 3, 5, 7] and b = [1, 4, 6, 8]. You want to test if sample a tends to have higher values than b. Which scipy Mann-Whitney U test call is correct?

hard

A. mannwhitneyu(a, b, alternative='greater')

B. mannwhitneyu(a, b, alternative='less')

C. mannwhitneyu(a, b, alternative='two-sided')

D. mannwhitneyu(b, a, alternative='greater')

Solution

1. Step 1: Define the hypothesis direction

   We want to test if a tends to have higher values than b, so the alternative hypothesis is 'greater'.

2. Step 2: Choose correct function call

   The call should be mannwhitneyu(a, b, alternative='greater') to test if a is stochastically greater than b.

3. Final Answer:

   mannwhitneyu(a, b, alternative='greater') -> Option A

4. Quick Check:

   Test if a > b = A [OK]

Hint: Use 'alternative="greater"' when testing if first sample is larger [OK]

Common Mistakes:

• Swapping sample order and alternative incorrectly
• Using 'less' when testing for greater
• Choosing 'two-sided' when direction matters